The excise duty on a packet of 20 cigarettes is being increased by 50c, including VAT, with a pro-rata increase on other tobacco products.
The measure, announced by Minister for Finance Michael Noonan, is the only tax increase in the Budget.
It will take effect from midnight tonight and will bring the price of cigarettes to €10.50.
The minister said the measure will raise €61.4m in a full year.
The price of alcohol, diesel and petrol remain untouched.
Socialist Party TD Joe Higgins said increasing the price of a packet of cigarettes was likely to drive people to buy smuggled cigarettes.
He accused the Government of hypocrisy.
However, Fine Gael Jerry Buttimer said the tobacco industry was targetting young people and said they as TDs had a duty of care to deliver a tobacco-free Ireland.
He said he would like to see some of the money raised ring fenced for cessation programmes.
Independent TD Finian McGrath said a lot of drug dealers were moving into illegal cigarettes.
Tánaiste Joan Burton said pricing is a deterrent in spite of the smuggling threat.
In a statement this evening, the Royal College of Physicians of Ireland welcomed the increase in the price of tobacco tax, as recommended by the College's Policy Group on Tobacco in its pre-budget submission.
Chair of the Policy Group Dr Pat Doorley said that the impact of this increase will be far-reaching.
"Tobacco taxation is the single most effective way to reduce tobacco consumption, particularly in discouraging children to take up smoking.
"We would like to see the Government commit to a significant annual increase in tobacco taxation in order to achieve the goal of a Tobacco Free Ireland by 2025."
As it happened: Catch up with our Budget 2016 Live Tracker